Cymatics: Vibrating plates to the Hydrogen Electron Shell

I say that when a table is struck in different places, the dust that is upon it is reduced to various shapes of mounds and tiny hillocks …

― Leonardo Da Vinci,  early “cymatic” research.

Double Hexagon Cymatic Image, made with CymaScope, an advanced cymatic research instrument.

Cymatics is the study of acoustically generated modal vibrations—standing wave systems. Examples of cymatic research include subjecting water, sand, or other semi-solid media to sound frequencies or music and observing the pattern in the media. Depending on the media used and the frequency applied, the patterns that emerge assume a variety of forms. This fascinating field of acoustic research has yielded a myriad of scientific and mathematical breakthroughs. Cymatic research continues to reveal more insights into the nature of our electric universe by aiding scientists understanding of wave phenomena. Though cymatic research crosses over into many scientific fields, this article takes a brief look into one discovery born from cymatic research—the Schrödinger equation. Mathematical models born out of cymatics lead to our current understanding of the electron shells of atoms, thereby increasing our understanding of the nature of electricity itself.

What Is Cymatics?


cymatic image at 1760 hz
Cymatic image produced with 1760hz vibration

Cymatic research is the study of visual and mathematical patterns in standing wave systems. Look at the image above and notice the enigmatic pattern that is produced with nothing more than a tone generator, metal plate, and some sand. What exactly creates these visual forms? The “pictures” or patterns that emerge are the result of standing waves. When a tone is applied to a plate or other media, the media resonates and produces an up and down motion on fixed places on the plate. These waves occur between stationary nodes.

Standing wave image.
This disc is an excellent example of a standing wave. Notice how the waves do not travel longitudinally, they only oscillate up and down.

When media such as sand is added to one of these vibrating plates, it arranges itself along the stationary nodes of the standing wave. Similarly, patterns emerge from media like water because the vibrations can be easily viewed in the water itself and there is no need for any other additional media. The vibrating metal plate is a very popular means of producing cymatic images. These metal plates that are subjected to vibration with either tone generators or other means attached are called Chladni Plates, after 19th century acoustician and physicist Ernst Chladni. View the video below to see a Chladni plate vibrated with a violin bow string.

More advanced instrumentation has recently been developed to produce cymatic imagery. One instrument is the Cymascope. This instrument uses ultra-pure water to produce standing-wave imagery. The reason ultra-pure water is used is because of the surface-tension properties. According to it’s developers, the water’s high flexibility and fast-response to vibration make it well suited for vibrational research. The cymascope was used to capture the first image of the article, as well as the one below.

Cymascope image
Another example of a cymatic image captured with a cymascope.

Cymatic Research Leads to 2D Wave Model

At first glance, cymatic research usually appears curious but with no obvious applications. However, Ernst Chladni recognized the potential mathematical implications of two-dimensional standing waves.  Eventually, later mathematicians pushed these solutions to three dimensions.

The story begins with the acoustician named Ernst Chladni, who experimented with cymatic plates, as mentioned earlier. He thought that the wave forms that were produced must have some mathematical relationship to the vibrational tone he applied. He came up with approximate solutions to model the cymatic image shape but never solved the 2D wave function completely.

cymatic data from Chladni in german
In a publicly available lecture from Yale University, Dr. James McBride shows Chladni’s original cymatic data

After the Math was Solved, Schrödinger could model the electron shell

Despite Chladni being unable to solve the puzzling mathematical problem posed by his plates, others eventually did. Chladni’s 2D mathematical problems attracted a lot of eminent mathematicians like Leonhard Euler, Daniel Bernoulli, and Joseph-Louis LaGrange. Building upon the rough approximations between frequency and nodes that Chladni described, these mathematicians pushed the mathematics to the point of solving both 2D and 3D wave functions. Later, other mathematicians like Edmond LaGuerre and Adrien-Marie Legendre continued to perfect wave function mathematics. Professor McBride of Yale University explains how cymatic disks were used to help solve wave functions in this YouTube video.

In this way, cymatic research was the impetus for mathematicians to study the field of 3D waveform research, and this research was used by Schrödinger to write his famous wave equation.


“The solutions we get involve what are called spherical harmonics, and they’re 3D analogues of Chladni’s 2D figures….[Speaking of 3D wave functions] Schrödinger didn’t find these, he just looked them up. These guys had already done it from acoustics.”

-Professor John Mcbride, Yale University

Are current electron models accurate?

It should be clear by now that cymatics has lead to accurate generalized mathematical formulas for 2D and 3D waves. Whether or not these equations are being applied correctly is open to debate. Mainstream science is confident that the hydrogen electron shell can be modeled by a 3D wave equation. Alternatively, other scientists like Edwin Kaal believe that atoms take on geometric forms. In his view, the electron “shell” would not exist at all, and the modeling of electron shells with 3D wave models would not be accurate whatsoever.

Bearing this in mind, are there any scientific problems that the 3D wave model could explain? Our current understanding of light could be better explained with wave models. This topic falls outside the scope of this article in particular, which serves to lay a foundation for our understanding of 2D and 3D standing waves born out of cymatic research.


Cymatics Will Continue to Open Doors

Cymatics is a curious subject. Many have been enchanted by it’s ability to produce novel forms. In fact, many find the Chladni plate images and forms so mystifying that they find no need to research deeper. However, the more scientifically inclined researchers have taken the 2D waveforms and produced brilliant mathematical formulas with it. It is clear that cymatic research played a critical role in the development of the Schrödinger equation. The 2D waveforms produced on Chladni plates were the first rough-sketch of the formulas that embody our current models of both 2D and 3D waves. Where does the story end? Cymatics may be applicable in another field, light research.

In the next article, we will look at other standing wave phenomena, and plausible explanations for wave-particle duality. Specifically, we will see how scientists are using particle-wave behavior to create life-size analogues of some quantum behavior. This research takes a remarkable look at one of the most puzzling “quantum weirdness” phenomena to date: the double slit experiment.

Readers are encouraged to send comments, questions, or inaccuracies to the author.


Violin bow Chladni plate video – A demonstration of sand forming cymatic patterns on a metal plate. From the film Inner Worlds Outer Worlds. Author: SpiritFilms

Video from Yale Open Courses – Chladni Figures and One-Electron Atoms, Professor James McBride, 2009

John Stuart Reid Quote -sourced from

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